Evaluating Overfit and Underfit in Models of Network Community Structure

A common data mining task on networks is community detection, which seeks an unsupervised decomposition of a network into structural groups based on statistical regularities in the network's connectivity. Although many methods exist, the No Free Lunch theorem for community detection implies that each makes some kind of tradeoff, and no algorithm can be optimal on all inputs. Thus, different algorithms will over or underfit on different inputs, finding more, fewer, or just different communities than is optimal, and evaluation methods that use a metadata partition as a ground truth will produce misleading conclusions about general accuracy. Here, we present a broad evaluation of over and underfitting in community detection, comparing the behavior of 16 state-of-the-art community detection algorithms on a novel and structurally diverse corpus of 406 real-world networks. We find that (i) algorithms vary widely both in the number of communities they find and in their corresponding composition, given the same input, (ii) algorithms can be clustered into distinct high-level groups based on similarities of their outputs on real-world networks, and (iii) these differences induce wide variation in accuracy on link prediction and link description tasks. We introduce a new diagnostic for evaluating overfitting and underfitting in practice, and use it to roughly divide community detection methods into general and specialized learning algorithms. Across methods and inputs, Bayesian techniques based on the stochastic block model and a minimum description length approach to regularization represent the best general learning approach, but can be outperformed under specific circumstances. These results introduce both a theoretically principled approach to evaluate over and underfitting in models of network community structure and a realistic benchmark by which new methods may be evaluated and compared.Comment: 22 pages, 13 figures, 3 table

Multi-view Graph Convolutional Networks with Differentiable Node Selection

Multi-view data containing complementary and consensus information can facilitate representation learning by exploiting the intact integration of multi-view features. Because most objects in real world often have underlying connections, organizing multi-view data as heterogeneous graphs is beneficial to extracting latent information among different objects. Due to the powerful capability to gather information of neighborhood nodes, in this paper, we apply Graph Convolutional Network (GCN) to cope with heterogeneous-graph data originating from multi-view data, which is still under-explored in the field of GCN. In order to improve the quality of network topology and alleviate the interference of noises yielded by graph fusion, some methods undertake sorting operations before the graph convolution procedure. These GCN-based methods generally sort and select the most confident neighborhood nodes for each vertex, such as picking the top-k nodes according to pre-defined confidence values. Nonetheless, this is problematic due to the non-differentiable sorting operators and inflexible graph embedding learning, which may result in blocked gradient computations and undesired performance. To cope with these issues, we propose a joint framework dubbed Multi-view Graph Convolutional Network with Differentiable Node Selection (MGCN-DNS), which is constituted of an adaptive graph fusion layer, a graph learning module and a differentiable node selection schema. MGCN-DNS accepts multi-channel graph-structural data as inputs and aims to learn more robust graph fusion through a differentiable neural network. The effectiveness of the proposed method is verified by rigorous comparisons with considerable state-of-the-art approaches in terms of multi-view semi-supervised classification tasks

Band gap prediction for large organic crystal structures with machine learning

Machine-learning models are capable of capturing the structure-property relationship from a dataset of computationally demanding ab initio calculations. Over the past two years, the Organic Materials Database (OMDB) has hosted a growing number of calculated electronic properties of previously synthesized organic crystal structures. The complexity of the organic crystals contained within the OMDB, which have on average 82 atoms per unit cell, makes this database a challenging platform for machine learning applications. In this paper, the focus is on predicting the band gap which represents one of the basic properties of a crystalline materials. With this aim, a consistent dataset of 12 500 crystal structures and their corresponding DFT band gap are released, freely available for download at https://omdb.mathub.io/dataset. An ensemble of two state-of-the-art models reach a mean absolute error (MAE) of 0.388 eV, which corresponds to a percentage error of 13% for an average band gap of 3.05 eV. Finally, the trained models are employed to predict the band gap for 260 092 materials contained within the Crystallography Open Database (COD) and made available online so that the predictions can be obtained for any arbitrary crystal structure uploaded by a user.Comment: 10 pages, 6 figure

Unsupervised multiple kernel learning approaches for integrating molecular cancer patient data

Cancer is the second leading cause of death worldwide. A characteristic of this disease is its complexity leading to a wide variety of genetic and molecular aberrations in the tumors. This heterogeneity necessitates personalized therapies for the patients. However, currently defined cancer subtypes used in clinical practice for treatment decision-making are based on relatively few selected markers and thus provide only a coarse classifcation of tumors. The increased availability in multi-omics data measured for cancer patients now offers the possibility of defining more informed cancer subtypes. Such a more fine-grained characterization of cancer subtypes harbors the potential of substantially expanding treatment options in personalized cancer therapy. In this thesis, we identify comprehensive cancer subtypes using multidimensional data. For this purpose, we apply and extend unsupervised multiple kernel learning methods. Three challenges of unsupervised multiple kernel learning are addressed: robustness, applicability, and interpretability. First, we show that regularization of the multiple kernel graph embedding framework, which enables the implementation of dimensionality reduction techniques, can increase the stability of the resulting patient subgroups. This improvement is especially beneficial for data sets with a small number of samples. Second, we adapt the objective function of kernel principal component analysis to enable the application of multiple kernel learning in combination with this widely used dimensionality reduction technique. Third, we improve the interpretability of kernel learning procedures by performing feature clustering prior to integrating the data via multiple kernel learning. On the basis of these clusters, we derive a score indicating the impact of a feature cluster on a patient cluster, thereby facilitating further analysis of the cluster-specific biological properties. All three procedures are successfully tested on real-world cancer data. Comparing our newly derived methodologies to established methods provides evidence that our work offers novel and beneficial ways of identifying patient subgroups and gaining insights into medically relevant characteristics of cancer subtypes.Krebs ist eine der häufigsten Todesursachen weltweit. Krebs ist gekennzeichnet durch seine Komplexität, die zu vielen verschiedenen genetischen und molekularen Aberrationen im Tumor führt. Die Unterschiede zwischen Tumoren erfordern personalisierte Therapien für die einzelnen Patienten. Die Krebssubtypen, die derzeit zur Behandlungsplanung in der klinischen Praxis verwendet werden, basieren auf relativ wenigen, genetischen oder molekularen Markern und können daher nur eine grobe Unterteilung der Tumoren liefern. Die zunehmende Verfügbarkeit von Multi-Omics-Daten für Krebspatienten ermöglicht die Neudefinition von fundierteren Krebssubtypen, die wiederum zu spezifischeren Behandlungen für Krebspatienten führen könnten. In dieser Dissertation identifizieren wir neue, potentielle Krebssubtypen basierend auf Multi-Omics-Daten. Hierfür verwenden wir unüberwachtes Multiple Kernel Learning, welches in der Lage ist mehrere Datentypen miteinander zu kombinieren. Drei Herausforderungen des unüberwachten Multiple Kernel Learnings werden adressiert: Robustheit, Anwendbarkeit und Interpretierbarkeit. Zunächst zeigen wir, dass die zusätzliche Regularisierung des Multiple Kernel Learning Frameworks zur Implementierung verschiedener Dimensionsreduktionstechniken die Stabilität der identifizierten Patientengruppen erhöht. Diese Robustheit ist besonders vorteilhaft für Datensätze mit einer geringen Anzahl von Proben. Zweitens passen wir die Zielfunktion der kernbasierten Hauptkomponentenanalyse an, um eine integrative Version dieser weit verbreiteten Dimensionsreduktionstechnik zu ermöglichen. Drittens verbessern wir die Interpretierbarkeit von kernbasierten Lernprozeduren, indem wir verwendete Merkmale in homogene Gruppen unterteilen bevor wir die Daten integrieren. Mit Hilfe dieser Gruppen definieren wir eine Bewertungsfunktion, die die weitere Auswertung der biologischen Eigenschaften von Patientengruppen erleichtert. Alle drei Verfahren werden an realen Krebsdaten getestet. Den Vergleich unserer Methodik mit etablierten Methoden weist nach, dass unsere Arbeit neue und nützliche Möglichkeiten bietet, um integrative Patientengruppen zu identifizieren und Einblicke in medizinisch relevante Eigenschaften von Krebssubtypen zu erhalten

Feature and Decision Level Fusion Using Multiple Kernel Learning and Fuzzy Integrals

The work collected in this dissertation addresses the problem of data fusion. In other words, this is the problem of making decisions (also known as the problem of classification in the machine learning and statistics communities) when data from multiple sources are available, or when decisions/confidence levels from a panel of decision-makers are accessible. This problem has become increasingly important in recent years, especially with the ever-increasing popularity of autonomous systems outfitted with suites of sensors and the dawn of the ``age of big data.\u27\u27 While data fusion is a very broad topic, the work in this dissertation considers two very specific techniques: feature-level fusion and decision-level fusion. In general, the fusion methods proposed throughout this dissertation rely on kernel methods and fuzzy integrals. Both are very powerful tools, however, they also come with challenges, some of which are summarized below. I address these challenges in this dissertation. Kernel methods for classification is a well-studied area in which data are implicitly mapped from a lower-dimensional space to a higher-dimensional space to improve classification accuracy. However, for most kernel methods, one must still choose a kernel to use for the problem. Since there is, in general, no way of knowing which kernel is the best, multiple kernel learning (MKL) is a technique used to learn the aggregation of a set of valid kernels into a single (ideally) superior kernel. The aggregation can be done using weighted sums of the pre-computed kernels, but determining the summation weights is not a trivial task. Furthermore, MKL does not work well with large datasets because of limited storage space and prediction speed. These challenges are tackled by the introduction of many new algorithms in the following chapters. I also address MKL\u27s storage and speed drawbacks, allowing MKL-based techniques to be applied to big data efficiently. Some algorithms in this work are based on the Choquet fuzzy integral, a powerful nonlinear aggregation operator parameterized by the fuzzy measure (FM). These decision-level fusion algorithms learn a fuzzy measure by minimizing a sum of squared error (SSE) criterion based on a set of training data. The flexibility of the Choquet integral comes with a cost, however---given a set of N decision makers, the size of the FM the algorithm must learn is 2N. This means that the training data must be diverse enough to include 2N independent observations, though this is rarely encountered in practice. I address this in the following chapters via many different regularization functions, a popular technique in machine learning and statistics used to prevent overfitting and increase model generalization. Finally, it is worth noting that the aggregation behavior of the Choquet integral is not intuitive. I tackle this by proposing a quantitative visualization strategy allowing the FM and Choquet integral behavior to be shown simultaneously

Optimal regularizations for data generation with probabilistic graphical models

Understanding the role of regularization is a central question in Statistical Inference. Empirically, well-chosen regularization schemes often dramatically improve the quality of the inferred models by avoiding overfitting of the training data. We consider here the particular case of L 2 and L 1 regularizations in the Maximum A Posteriori (MAP) inference of generative pairwise graphical models. Based on analytical calculations on Gaussian multivariate distributions and numerical experiments on Gaussian and Potts models we study the likelihoods of the training, test, and 'generated data' (with the inferred models) sets as functions of the regularization strengths. We show in particular that, at its maximum, the test likelihood and the 'generated' likelihood, which quantifies the quality of the generated samples, have remarkably close values. The optimal value for the regularization strength is found to be approximately equal to the inverse sum of the squared couplings incoming on sites on the underlying network of interactions. Our results seem largely independent of the structure of the true underlying interactions that generated the data, of the regularization scheme considered, and are valid when small fluctuations of the posterior distribution around the MAP estimator are taken into account. Connections with empirical works on protein models learned from homologous sequences are discussed

Design and HPC implementation of unsupervised Kernel methods in the context of molecular dynamics

The thesis represents an extensive research in the multidisciplinary domain formed by the cross contamination of unsupervised learning and molecular dynamics, two research elds that are coming close creating a breeding ground for valuable new concepts and methods. In this context, at rst, we describe a novel engine to perform large scale kernel k-means clustering. We introduce a two-fold approximation strategy to minimize the kernel k-means cost function in which the trade-off between accuracy and execution time is automatically ruled by the available system memory